Notions of computability at higher types I
نویسنده
چکیده
We discuss the conceptual problem of identifying the natural notions of computability at higher types (over the natural numbers). We argue for an eclectic approach, in which one considers a wide range of possible approaches to defining higher type computability and then looks for regularities. As a first step in this programme, we give an extended survey of the different strands of research on higher type computability to date, bringing together material from recursion theory, constructive logic and computer science. The paper thus serves as a reasonably complete overview of the literature on higher type computability. Two sequel papers will be devoted to developing a more systematic account of the material reviewed here.
منابع مشابه
Notions of computability at higher types II
In Part I of this series of papers [Lon01a] we gave a historical survey of the study of notions of higher-type computability. In the present paper and its sequel [Lon01b], we undertake a more systematic exposition of notions of higher-type computability, showing how many of the existing ideas and results can be fitted into a coherent framework. In Part II we will restrict our attention to notio...
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